We present the numerical results for the optical response of a hybrid asymmetric quantum dot-metal nanoparticle system driven by a strong optical field in the resonant case. We investigate the dependence of the real and imaginary parts of the probe beam conductivity on the pump intensity, on the interval between the surface of the metallic nanosphere and the quantum dot, and on the polarization direction of the applied electromagnetic field in the quasistatic limit. When the pump frequency is equal to the exciton transition frequency, we observe the complex Mollow absorption spectrum, consisting of a weak center peak and two Rabi sidebands having dispersive lineshapes. We see that one can suppress or enhance the probe absorption/dispersion spectra by varying the interval between the metal nanoparticle and the quantum dot, the polarization direction of the electromagnetic field, and the pump intensity.